A nonlinear creep model for surrounding rocks of tunnels based on kinetic energy theorem

The initiating condition for the accelerated creep of rocks has caused difficulty in analyzing the whole creep process.Moreover,the existing Nishihara model has evident shortcomings in describing the accelerated creep characteristics of the viscoplastic stage from the perspective of internal energy to analyze the mechanism of rock creep failure and determine the threshold of accelerated creep initiation.Based on the kinetic energy theorem,Perzyna viscoplastic theory,and the Nishihara model,a unified creep constitutive model that can describe the whole process of decaying creep,stable creep,and accelerated creep is established.Results reveal that the energy consumption and creep damage in the process of creep loading mainly come from the internal energy changes of geotechnical materials.The established creep model can not only describe the viscoelasticeplastic creep characteristics of rock,but also reflect the relationship between rock energy and creep deformation change.In addition,the research results provide a new method for determining the critical point of creep deformation and a new idea for studying the creep model and creep mechanical properties.

Energy average formula of photon gas rederived by using the generalised Hermann-Feynman theorem

By virtue of the generalised Hermann-Feynmam theorem we re-derive the energy average formula of photon gas. This is another useful application of the theorem.

Deriving Internal Energy by Virtue of Generalized Feynman-Hellmann Theorem for Mixed States

We show how to directly use the generalized Feynman-Hellmann theorem, which is suitable for mixed state ensemble average, to derive the internal energy of Hamiltonian systems. A concrete example, which is a two coupled harminic oscillators, is used for elucidating our approach.

NEW PRINCIPLES OF WORK AND ENERGY AS WELLAS POWER AND ENERGY RATE FORCONTINUUM FIELD THEORIES

New principles of work and energy as well as power and energy rate with cross terms for polar and nonlocal polar continuum field theories were presented and from them all corresponding equations of motion and boundary conditions as well as complete equations of energy and energy rate with the help of generalized Piola's theorems were naturally derived in all and without any additional requirement. Finally, some new balance laws of energy and energy rate for generalized continuum mechanics were established. The new principles of work and energy as well as power and energy rate with cross terms presented in this paper are believed to be new and they have corrected the incompleteness of all existing corresponding principles and laws without cross terms in literatures of generalized continuum field theories.

The Gap Labelling Integrated Density of States for a Quasi Crystal Universe Is Identical to the Observed 4.5 Percent Ordinary Energy Density of the Cosmos

Condense matter methods and mathematical models used in solving problems in solid state physics are transformed to high energy quantum cosmology in order to estimate the magnitude of the missing dark energy of the universe. Looking at the problem from this novel viewpoint was rewarded by a rather unexpected result, namely that the gap labelling method of integrated density of states for three dimensional icosahedral quasicrystals is identical to the previously measured and theoretically concluded ordinary energy density of the universe, namely a mere 4.5 percent of Einstein’s energy density, i.e. E(O) = mc2/22 where E is the energy, m is the mass and c is the speed of light. Consequently we conclude that the missing dark energy density must be E(D) = 1 - E(O) = mc2(21/22) in agreement with all known cosmological measurements and observations. This result could also be interpreted as a strong evidence for the self similarity of the geometry of spacetime, which is an expression of its basic fractal nature.

Energy dependence on the electric activities of a neuron

A nonlinear circuit can be designed by using inductor, resistor, capacitor and other electric devices, and the electromagnetic field energy can be released from the circuit in the oscillating state. The generation of spikes or bursting states in neurons could be energetically a costly process. Based on the Helmholtz＇s theorem, a Hamilton energy function is defined to detect the energy shift induced by transition of electric modes in a Hindmarsh–Rose neuron. It is found that the energy storage is dependent on the external forcing, and energy release is associated with the electric mode. As a result, the bursting state and chaotic state could be helpful to release the energy in the neuron quickly.

NEW PRINCIPLES OF POWER AND ENERGY RATE OF INCREMENTAL RATE TYPE FOR GENERALIZED CONTINUUM FIELD THEORIES

The aim of this paper is to establish new principles of power and energy rate of incremental type in generalized continuum mechanics BY combining new principles of virtual velocity and virtual angular velocity as well as of virtual stress anti virtual couple stress with c ross terms of incremental rate type a new principle of power anti energy rate of incremental rate type with cross terms for micropolar continuum field theories is presented and from it all corresponding equations of motion and boundary conditions as well as power and energy rate equations of incremental rate type for micropolar and nonlocal micropolar continua with the help of generalized Piola's theorems in all and without any additional requirement are derived. Complete results for micromorphic continua could be similarly derived. The derived results in the present paper are believed to be new. They could be used to establish corresponding finite element methods of incremental rate type for generalized continuum mechanics.

The Hydrogen Atom Fractal Spectra, the Missing Dark Energy of the Cosmos and Their Hardy Quantum Entanglement

In this letter, I outline the intimate connection between the fractal spectra of the exact solution of the hydrogen atom and the issue of the missing dark energy of the cosmos. A proposal for a dark energy reactor harnessing the dark energy of the Schrodinger wave via a quantum wave nondemolition measurement is also presented.

Application of Dvoretzky’s Theorem of Measure Concentration in Physics and Cosmology

Using Dvoretzky’s theorem in conjunction with Bohm’s picture of a quantum particle inside a guiding quantum wave akin to De Broglie-Bohm pilot wave we derive Einstein’s famous formula E = mc2 as the sum of two parts E(O) = mc2/22 of the quantum particle and E(D) = m c2 (21/22) of the quantum wave where m is the mass, c is the speed of light and E is the energy. In addition we look at the problem of black holes information in the presence of extra dimensions where it seems initially that extra dimensions would logically lead to a hyper-surface for a black hole and consequently a reduction of the corresponding information density due to the dilution effect of these additional dimensions. The present paper argues that the counterintuitive opposite of the above is what should be expected. Again this surprising result is a consequence of the same well known theorem on measure concentration due to I. Dvoretzky. We conclude that there are only two real applications of the theorem and we expect that many more applications in physics and cosmology will be found in due course.

Asking If the Existence of Vacuum Energy to Keep Computational “Bits” Present at Start of Cosmological Evolution, Even If Spatial Radius Goes to Zero, Not Planck Length, Is Possible

When initial radius Rinitial →0 if Stoica actually presents Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds. We present entanglement entropy in the early universe with a shrinking scale factor, due to Muller and Lousto, and show that there are consequences due to initial entangled SEntropy = 0.3r2h/a2 for a time dependent horizon radius rH = in cosmology, with (flat space conditions) for conformal time. Even if the 3 dimensional spatial length goes to zero, this construction preserves a minimum non-zero L vacuum energy, and in doing so keep the bits, for computational bits cosmological evolution even if Rinitial →0 . We state that the presence of computational bits is necessary for cosmological evolution to commence.

Hubble Scale Dark Energy Meets Nano Scale Casimir Energy and the Rational of Their T-Duality and Mirror Symmetry Equivalence

We establish that ordinary energy, Casimir energy and dark energy are not only interlinked but are basically the same thing separated merely by scale and topology. Casimir energy is essentially a nano scale spacetime phenomenon produced by the boundary condition of the two Casimir plates constituting the Casimir experimental set up for measuring the Casimir force. By contrast dark energy is the result of the cosmic boundary condition, i.e. the boundary of the universe. This one sided M?bius-like boundary located at vast cosmic distance and was comparable only to the Hubble radius scales of the universe. All the Casimir energy spreads out until the majority of it reaches the vicinity of the edge of the cosmos. According to a famous theorem due to the Ukrainian-Israeli scientist I. Dvoretzky, almost 96% of the total energy will be concentrated at the boundary of the universe, too far away to be measured directly. The rest of the accumulated Casimir energy density is consequently the nearly 4% to 4.5%, the existence of which is confirmed by various sophisticated cosmic measurements and observations. When all is said and done, the work is essentially yet another confirmation of Witten’s T-duality and mirror symmetry bringing nano scale and Hubble scale together in an unexpected magical yet mathematically rigorous way.

A Combined Heterotic String and Kähler Manifold Elucidation of Ordinary Energy,Dark Matter,Olbers’s Paradox and Pure Dark Energy Density of the Cosmos

We utilize the topological-geometrical structure imposed by the Heterotic superstring theory on spacetime in conjunction with the K3 Kähler manifold to explain the mysterious nature of dark matter and its coupling to the pure dark energy density of the cosmos. The analogous situations in the case of a Kerr black hole as well as the redundant components of the Riemannian tensor are pointed out and the final result was found to be in complete agreement with all previous theoretical ones as well as all recent accurate measurements and cosmic observations. We conclude by commenting briefly on the Cantorian model of Zitterbewegung and the connection between Olbers’s paradox and dark energy.

Basic quantities of the equation of state in isospin asymmetric nuclear matter

Based on the Hugenholtz-Van Hove theorem six basic quantities of the EoS in isospin asymmetric nuclear matter are expressed in terms of the nucleon kinetic energy t(k),the isospin symmetric and asymmetric parts of the single-nucleon potentials U_(0)(ρ,k)and U_(sym,i)(ρ,k).The six basic quantities include the quadratic symmetry energy E_(sym,2)(ρ),the quartic symmetry energy E_(sym,4)(ρ),their corresponding density slopes L_(2)(ρ)and L_(4)(ρ),and the incompressibility coefficients K_(2)(ρ)and K_(4)(ρ).By using four types of well-known effective nucleon-nucleon interaction models,namely the BGBD,MDI,Skyrme,and Gogny forces,the density-and isospin-dependent properties of these basic quantities are systematically calculated and their values at the saturation density q_(0)are explicitly given.The contributions to these quantities from t(k)U_(0)(ρ,k),and U_(sym,i)(ρ,k)are also analyzed at the norma nuclear density q_(0).It is clearly shown that the first-order asymmetric term U_(sym,1)(ρ,k)(also known as the symmetry potential in the Lane potential)plays a vital role in determining the density dependence of the quadratic symmetry energy E_(sym,2)(ρ).It is also shown that the contributions from the high-order asymmetric parts of the single-nucleon potentials(U_(sym,i)(ρ,k)with i>1)cannot be neglected in the calculations of the other five basic quantities Moreover,by analyzing the properties of asymmetric nuclear matter at the exact saturation densityρ_(sat)(δ),the corresponding quadratic incompressibility coefficient is found to have a simple empirical relation K_(sat,2)=K_(2)(ρ_(0))-4.14L_(2)(ρ_(0))

Thermal-induced snap-through buckling of simply-supported functionally graded beams

The instability of functionally graded material(FGM)structures is one of the major threats to their service safety in engineering applications.This paper aims to clarify a long-standing controversy on the thermal instability type of simply-supported FGM beams.First,based on the Euler-Bernoulli beam theory and von K′arm′an geometric nonlinearity,a nonlinear governing equation of simply-supported FGM beams under uniform thermal loads by Zhang’s two-variable method is formulated.Second,an approximate analytic solution to the nonlinear integro-differential boundary value problem under a thermal-induced inhomogeneous force boundary condition is obtained by using a semiinverse method when the coordinate axis is relocated to the bending axis(physical neutral plane),and then the analytical predictions are verified by the differential quadrature method(DQM).Finally,based on the free energy theorem,it is revealed that the symmetry breaking caused by the material inhomogeneity can make the simply-supported FGM beam under uniform thermal loads occur snap-through postbuckling only in odd modes;furthermore,the nonlinear critical load of thermal buckling varies non-monotonically with the functional gradient index due to the stretching-bending coupling effect.These results are expected to provide new ideas and references for the design and regulation of FGM structures.

PHRAGMEN－LINDELOF ALTERNATIVE RESULTS FOR THE INITIAL BOUNDARY PROBLEM OF STOKES EQUATION

In this paper we prove Phragmen-Lindelof type alternative.for foe initial boundaryproblem of Stokes equation, i. e. we show that the energy expression for the solutionof the initial boundary problem must either grow exponentially or decay exponentiallywilh axial distance from the end of a semi-infinite strip. For the case of decay, we alsoestablish the pointwise estimate for the maximum module of the Stokes .flow andpresent a method for obtaining explicit bounds for the total energy.

Global Static Solutions of the Spherically Symmetric Vlasov-Einstein-Maxwell (VEM) System for Low Charge

We consider the VEM system in the context of spherical symmetry and we try to establish a global static solutions with isotropic pressure that approaches Minkowski spacetime at infinity and have a regular center. To be in accordance with numerical investigation we take here low charge particles.

THE DERIVATION OF EXACT STATIC CONDITIONS AT THE CORNER POINTS FOR THE BENDING OF THICK RECTANGULAR PLATES

In this paper, exact static conditions at the corner points for the bending of thickrectangular ptates are strictly. derived from the theorem of minimum potentialenerg[1].

Bayes Theorem Based Virtual Machine Scheduling for Optimal Energy Consumption

This paper proposes an algorithm for scheduling Virtual Machines(VM)with energy saving strategies in the physical servers of cloud data centers.Energy saving strategy along with a solution for productive resource utilizationfor VM deployment in cloud data centers is modeled by a combination of“VirtualMachine Scheduling using Bayes Theorem”algorithm(VMSBT)and Virtual Machine Migration(VMMIG)algorithm.It is shown that the overall data center’sconsumption of energy is minimized with a combination of VMSBT algorithmand Virtual Machine Migration(VMMIG)algorithm.Virtual machine migrationbetween the active physical servers in the data center is carried out at periodicalintervals as and when a physical server is identified to be under-utilized.In VMscheduling,the optimal data centers are clustered using Bayes Theorem and VMsare scheduled to appropriate data center using the selection policy that identifiesthe cluster with lesser energy consumption.Clustering using Bayes rule minimizesthe number of server choices for the selection policy.Application of Bayestheorem in clustering has enabled the proposed VMSBT algorithm to schedule thevirtual machines on to the physical server with minimal execution time.The proposedalgorithm is compared with other energy aware VM allocations algorithmsviz.“Ant-Colony”optimization-based(ACO)allocation scheme and“min-min”scheduling algorithm.The experimental simulation results prove that the proposedcombination of‘VMSBT’and‘VMMIG’algorithm outperforms othertwo strategies and is highly effective in scheduling VMs with reduced energy consumptionby utilizing the existing resources productively and by minimizing thenumber of active servers at any given point of time.

Variation of Vacuum Energy if Scale Factor Becomes Infinitely Small, with Fixed Entropy Due to a Non Pathological Big Bang Singularity Accessible to Modified Einstein Equations

When initial radius Rinitial 0 if Stoica actually derived Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds. The implications of Rinitial 0 are the first part of this manuscript. Then the resolution is alluded to by work from Muller and Lousto, as to implications of entanglement entropy. We present entanglement entropy in the early universe with a steadily shrinking scale factor, due to work from Muller and Lousto, and show that there are consequences due to initial entanged Sentropy=0.3rH2/a2 for a time dependent horizon radius rH in cosmology, with for flat space conditions rH= for conformal time. In the case of a curved, but not flat space version of entropy, we look at vacuum energy as proportional to the inverse of scale factor squared times the inverse of initial entropy, effectively when there is no initial time in line with ~H2/G H≈a-1. The consequences for this initial entropy being entangled are elaborated in this manuscript. No matter how small the length gets, Sentropy if it is entanglement entropy, will not go to zero. The requirement is that the smallest length of time, t, re scaled does not go to zero. Even if the length goes to zero. This preserves a minimum non zero vacuum energy, and in doing so keep the bits, for computational bits cosmological evolution even if Rinitial 0.

An Inquiry into Two Intriguing Values of the Critical Current Density of Bi-2212

The empirically reported values of the critical current density (jc) of Bi-2212 as 2.4 × 105 (jc1;Sample 1) and 1.0 × 106 A/cm2 (jc2;Sample 2) are intriguing because both of them correspond to the same values of the temperature T = 4.2 K and the applied magnetic field H = 12 × 104 G. This difference is conventionally attributed to such factors—not all of which are quantifiable—as the geometry, dimensions and the nature of dopants and the manners of preparation of the samples which cause their granular structures, grain boundaries, alignment of the grains and so on to differ. Based on the premise that the chemical potential μ subsumes most of these features, given herein is a novel explanation of the said results in terms of the values of μ of the two samples. This paper revisits the problem that was originally addressed in [Malik G.P., Varma V.S. (2020) WJCMP, 10, 53-70] in the more accurate framework of a subsequent paper [Malik G.P., Varma V.S. (2021) JSNM, 34, 1551-1561]. Besides, it distinguishes between the contributions of the electro-electron (e-e) and the hole-hole (h-h) pairs to jc—a feature to which no heed was paid earlier. The essence of our findings is that the jcs of the two samples differ because they are characterized by different values of the primary variables μi and , where is the effective mass of a charge-carrier and me is the free-electron mass and i = 1 and 2 denote Sample 1 and Sample 2, respectively. In the scenario of the charge-carriers being predominantly h-h pairs, the values of these parameters are estimated to be: μ1 ≈ 12.3 meV, η1 ≈ 0.58;μ2 ≈ 22.7 meV, η2 ≈ 0.94. Following from these and similar estimates when the charge-carriers are e-e pairs, given below for each sample are the detailed results for the values of the secondary variables viz. the number density of the charge-carriers and their critical velocity, the number of occupied Landau levels and the magnetic interaction parameter.